The use of a recently decommissioned 15-meters long twin aperture LHC superconducting magnet prototype having a transverse magnetic field B ~ 9.5 T provides the unique opportunity for the construction of a new powerful experiment to measure the Vacuum Magnetic Birefringence (VMB). The values or the limit values of the mass and of the coupling constant to two photons of possible dark matter candidates such as axions are aimed to be deduced from such an experiment. In this article, the technical feasibility study of a new setup to measure the VMB will be presented. It is based on a linear optical resonant cavity housed in the LHC superconducting dipole prototype. The mechanical integrations of the optical components inside the magnet aperture as well as the optical detection principles will be presented. A comparison of the expected performances with respect to the present reference results for this type of experiment will also be given.
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